Mammal Stroke Volume

Data

Predictors: body mass interacting with habitat.

Read in data

mammal_sv <- read.csv("data/sv.csv")

Notes

log10sv is the base-10 logarithm of stroke volume in ml

Cleaning

Rename some variables and create species name from genus and species.

mammal_sv <- mammal_sv %>%
  rename(source = Source,
         order = order.corrected,
         mass.kg = body.mass..kg.) %>%
  mutate(order = str_to_title(order),
         genus = str_to_title(genus),
         animal = paste(genus, species),
         above.10kg = ifelse(mass.kg >= 10, 'Larger', 'Smaller'))

Keep only variables we will be using. And factor() “chr” variables.

mammal_sv <- mammal_sv %>%
  dplyr::select(order,
                genus,
                species, 
                common.name,
                mass.kg,
                log10.body.mass,
                log10sv,
                habitat,
                source,
                animal,
                above.10kg
         ) %>%
  mutate(across(where(is.character), factor)) %>%
  arrange(order, genus, species)

Viz

A few quick graphs just to make sure the data are looking as we expect (error checking).

my_scatter_plot <- gf_point(log10sv ~ log10.body.mass | habitat,
         color = ~order,
         # size = ~parse_number(n_animals),
         data = mammal_sv,
         alpha = 0.5) %>%
  gf_theme(legend.position = 'bottom',
           legend.title = element_text(size = 8),
           legend.text = element_text(size = 6)) %>%
  gf_theme(scale_color_viridis_d('Order')) %>%
  gf_labs(x = 'Log10(Mass (kg))',
          y = 'Log10(SV (ml))')

my_scatter_plot

plotly::ggplotly(my_scatter_plot) %>%
  plotly::layout(legend = list(#orientation = 'h',
                               font = list(size = 6)))

Notes: If we wanted to use for web or publication, we would refine. We can edit what info is shown when you hover over a data point, change color scheme, legend, etc.

GLS

Will not account for phylogeny at all in the model structure. Predictors: body mass interacting with habitat. Weight by number of individuals (if have data later, don’t have it now)?

lm_model <- lm(log10sv ~ log10.body.mass * habitat,
                 data = mammal_sv)
summary(lm_model)

## 
## Call:
## lm(formula = log10sv ~ log10.body.mass * habitat, data = mammal_sv)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38559 -0.09944 -0.03216  0.14260  0.36045 
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  0.16485    0.20949   0.787    0.439    
## log10.body.mass              0.99959    0.09295  10.754 7.25e-11 ***
## habitatland                 -0.19610    0.21600  -0.908    0.373    
## log10.body.mass:habitatland  0.04781    0.09705   0.493    0.627    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1745 on 25 degrees of freedom
## Multiple R-squared:  0.9853, Adjusted R-squared:  0.9836 
## F-statistic: 559.1 on 3 and 25 DF,  p-value: < 2.2e-16

tab_model(lm_model)

	log 10 sv
Predictors	Estimates	CI	p
(Intercept)	0.16	-0.27 – 0.60	0.439
log10.body.mass	1.00	0.81 – 1.19	<0.001
habitat [land]	-0.20	-0.64 – 0.25	0.373
log10.body.mass * habitat [land]	0.05	-0.15 – 0.25	0.627
Observations	29
R² / R² adjusted	0.985 / 0.984

lm_anova_results <- car::Anova(lm_model)
pander(lm_anova_results)

Anova Table (Type II tests)
	Sum Sq	Df	F value	Pr(>F)
log10.body.mass	46.39	1	1524	6.308e-24
habitat	0.04624	1	1.519	0.2292
log10.body.mass:habitat	0.007388	1	0.2427	0.6265
Residuals	0.761	25	NA	NA

Model Assessment

lm_preds <- predict(lm_model, se.fit = TRUE)

mammal_sv <- mammal_sv  %>% mutate(lm_resids = resid(lm_model),
         lm_fitted = lm_preds$fit,
         lm_fit_lo = lm_preds$fit + 1.96*lm_preds$se.fit,
         lm_fit_hi = lm_preds$fit - 1.96*lm_preds$se.fit)
gf_point(lm_resids ~ lm_fitted, data = mammal_sv)

acf(resid(lm_model))

gf_dhistogram(~lm_resids, data = mammal_sv,
              bins = 7) %>%
  gf_fitdistr()

Model Predictions

Any predictors not shown in a plot are held constant at their mean or most common value.

gf_line(lm_fitted ~ log10.body.mass,
         color = ~habitat,
         data = mammal_sv) %>%
  gf_ribbon(lm_fit_lo + lm_fit_hi ~ log10.body.mass,
            color = ~habitat, fill = ~habitat) %>% 
  gf_theme(scale_color_manual(values = my_colors)) %>%
  gf_theme(scale_fill_manual(values = my_colors))

gf_point(log10sv ~ lm_fitted, data = mammal_sv,
         alpha = 0.1) %>%
  gf_labs(y = 'Observed log10(fH)',
          x = 'Model-predicted log10(fH)',
          title = 'Linear Regresssion (no phylogeny)') %>%
  gf_abline(slope = 1, intercept = 0, color = 'black', linetype = 'dashed')

Can refine the plot of predictions later on.

Mixed-effects model

Will include nested random effects of order/family/genus/species, expecting similarity of observations based on a hierarchy of phylogenetic relatedness, but not in a specified/structured way; only groupings are used, with no sense of (for example) the fact that two orders are thought to be “further” apart than any other two.

re_model <- glmmTMB(log10sv ~ log10.body.mass * habitat +
                      (1 | order/genus/species),
                 data = mammal_sv)
summary(re_model)

##  Family: gaussian  ( identity )
## Formula:          
## log10sv ~ log10.body.mass * habitat + (1 | order/genus/species)
## Data: mammal_sv
## 
##      AIC      BIC   logLik deviance df.resid 
##     -9.5      1.5     12.7    -25.5       21 
## 
## Random effects:
## 
## Conditional model:
##  Groups                Name        Variance  Std.Dev. 
##  species:(genus:order) (Intercept) 1.740e-03 4.172e-02
##  genus:order           (Intercept) 2.360e-02 1.536e-01
##  order                 (Intercept) 8.935e-11 9.452e-06
##  Residual                          1.579e-03 3.973e-02
## Number of obs: 29, groups:  
## species:(genus:order), 29; genus:order, 27; order, 9
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00158 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  0.16485    0.19699   0.837    0.403    
## log10.body.mass              0.99959    0.08741  11.436   <2e-16 ***
## habitatland                 -0.17116    0.20442  -0.837    0.402    
## log10.body.mass:habitatland  0.03755    0.09173   0.409    0.682    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

tab_model(re_model)

	log 10 sv
Predictors	Estimates	CI	p
(Intercept)	0.16	-0.22 – 0.55	0.403
log10.body.mass	1.00	0.83 – 1.17	<0.001
habitat [land]	-0.17	-0.57 – 0.23	0.402
log10.body.mass * habitat [land]	0.04	-0.14 – 0.22	0.682
Random Effects
σ²	0.00
τ₀₀ _{species:(genus:order)}	0.00
τ₀₀ _genus:order	0.02
τ₀₀ _order	0.00
N _species	28
N _genus	27
N _order	9
Observations	29
Marginal R² / Conditional R²	0.999 / NA

re_anova_results <- car::Anova(re_model)
pander(re_anova_results)

Analysis of Deviance Table (Type II Wald chisquare tests)
	Chisq	Df	Pr(>Chisq)
log10.body.mass	1520	1	0
habitat	1.576	1	0.2093
log10.body.mass:habitat	0.1676	1	0.6823

Model Assessment

re_ave_preds <- predict(re_model, 
                    se.fit = TRUE,
                    re.form = ~0)
re_ind_preds <- predict(re_model,
                        se.fit = TRUE,
                        re.form = NULL)
mammal_sv <- mammal_sv %>%
  mutate(re_resids = resid(re_model),
         re_ind_fitted = re_ind_preds$fit,
         re_ave_fitted = re_ave_preds$fit,
         re_ave_lo = re_ave_preds$fit - 1.96*re_ave_preds$se.fit,
         re_ave_hi = re_ave_preds$fit + 1.96*re_ave_preds$se.fit)
gf_point(re_resids ~ re_ind_fitted, data = mammal_sv)

# save fitted model and data
saveRDS(mammal_sv, 'fitted-models/sv-data.RDS')
saveRDS(re_model, 'fitted-models/sv-re-model.RDS')


acf(resid(re_model))
acf(resid(re_model))

gf_dhistogram(~re_resids, data = mammal_sv,
              bins = 7) %>%
  gf_fitdistr()

Predictions from Model

gf_line(re_ave_fitted ~ log10.body.mass,
         color = ~habitat,
         data = mammal_sv) %>%
  gf_ribbon(re_ave_lo + re_ave_hi ~ log10.body.mass,
            color = ~habitat, fill = ~habitat) %>%
  gf_theme(scale_color_manual(values = my_colors)) %>%
  gf_theme(scale_fill_manual(values = my_colors))

gf_point(log10sv ~ re_ind_fitted, data = mammal_sv,
         alpha = 0.1) %>%
  gf_labs(y = 'Observed log10(sv)',
          x = 'Model-predicted, Species-specific log10(sv)',
          title = 'Mixed-effects Model (RE of Order/Genus/Species)') %>%
  gf_abline(slope = 1, intercept = 0, color = 'black', linetype = 'dashed')

The graph above is a bit “cheating” as we have a random effect of species, but there are only 1-2 measurements for most of the species (nearly guaranteeing that our estimates will be nearly perfect). What if we also check out the predictions accounting for the modeled effects of Order and Genus, but predicting for the “average” species in each Genus?

gf_line(re_ave_fitted ~ log10.body.mass,
         color = ~habitat,
         data = mammal_sv) %>%
  gf_ribbon(re_ave_lo + re_ave_hi ~ log10.body.mass,
            color = ~habitat, fill = ~habitat) %>%
  gf_theme(scale_color_manual(values = my_colors)) %>%
  gf_theme(scale_fill_manual(values = my_colors))

gf_point(log10sv ~ re_ind_fitted, data = mammal_sv,
         alpha = 0.1) %>%
  gf_labs(y = 'Observed log10(fH)',
          x = 'Model-predicted, Order-specific log10(fH)',
          title = 'Mixed-effects Model (RE of Order/Genus)') %>%
  gf_abline(slope = 1, intercept = 0, color = 'black', linetype = 'dashed')

PGLS

#Read in the trees from Upham et al

tree_path <- paste("data/upham-trees/Completed_5911sp_topoCons_FBDasZhouEtAl")
tree_files <- list.files(tree_path)


all_trees <- list()

for (i in 1:length(tree_files)){
  all_trees[[i]] <- read.tree(paste0(tree_path, '/',
                                     tree_files[i]))
  if (i == 1){
    treeset <- all_trees[[i]]
  }else{
    treeset <- c(treeset, all_trees[[i]])
  }
}

all_tip_labels <- purrr::map(treeset, "tip.label")
all_tip_labels <- purrr::map(all_tip_labels,
                             function(x) 
                               stringr::str_replace_all(x, pattern = '_',
                                                      replacement = ' '))

# get list of species that are in ALL the trees
for (t in 1:length(all_tip_labels)){
  if (t == 1){
    tip_labs <- all_tip_labels[[t]]
  }else{
    tip_labs <- intersect(tip_labs, all_tip_labels[[t]])
  }
}

                            
# keep only the species in mammal_sv that are in all the trees
# on 6/17 this removes NO species.
pgls_data <- mammal_sv %>%
  mutate(animal = as.character(animal)) %>%
  filter(animal %in% tip_labs) %>%
  droplevels()


taxonomy <- read_csv('data/upham-trees/taxonomy_mamPhy_5911species.csv')

Fit models, one model for every tree in our list.

pgls_models <- list()

for (t in c(1:length(treeset))){
  # make sure there is only one row of data per species
  pgls_rep_data <- pgls_data %>% 
    group_by(animal) %>%
    sample_n(1) %>%
    ungroup
  
  
  #Reduce the tree to only include those species in the data set
  refit_tree <- treeset[[t]]
  refit_tree$tip.label <- str_replace_all(refit_tree$tip.label, '_', ' ')
  refit_tree <- drop.tip(refit_tree, 
                         setdiff(refit_tree$tip.label, 
                                 unique(pgls_rep_data %>% pull(animal))))
  
  #Order the data set so that it is in the same order as the tip labels of the tree
  pgls_rep_data <- left_join(data.frame(tree.tip.label = refit_tree$tip.label),
                             pgls_rep_data,
                             by = c('tree.tip.label' = 'animal'),
                             keep = TRUE)
  
  # fit the model
 pgls_models[[t]] <- tryCatch({
    fittd <- gls(log10sv ~ log10.body.mass * habitat,
                 correlation = corPagel(value = 0.8, 
                                        phy = refit_tree, 
                                        fixed = FALSE, 
                                        form = ~animal),
                 data = pgls_rep_data)
  },
  error = function(cond){
    message(paste('PGLS fit failed for tree', t))
    return(NULL)
  }
  )
}

pgls_models <- pgls_models[!sapply(pgls_models, is.null)]

Note: we tried to fit 101 PGLS models (each with a different tree); of these, model fitting failed for 4.

Combine the many PGLS model runs together into one summary combined model according to Rubin’s rule.

# as.mira takes the list of models and create an object to be used by the mice package
pgls_mira <- as.mira(pgls_models)  
# # pool summarise the models using Rubin's rule corrected for small samples
pooled_pgls   <- pool(pgls_mira)
pooled_pgls_summ <- summary(pooled_pgls, type = 'all', conf.int = TRUE)

pander(pooled_pgls_summ %>% dplyr::select(term, estimate, std.error, `2.5 %`, `97.5 %`, lambda, fmi))

Table continues below
term	estimate	std.error	2.5 %	97.5 %
(Intercept)	0.2041	0.21	-0.2354	0.6436
log10.body.mass	0.9929	0.09319	0.7988	1.187
habitatland	-0.2378	0.2206	-0.6989	0.2234
log10.body.mass:habitatland	0.05945	0.09692	-0.1422	0.2611

lambda	fmi
0.1758	0.2507
0.1154	0.1908
0.1604	0.2354
0.09824	0.1737

# this depends on inner workings of package car found in gls-utils.R
# it used to work without all this, in summer 2021 stopped
pgls_anova <- Anova(pgls_mira)
pander(pgls_anova)

Analysis of Deviance Table (Type II tests) (continued below)
	F	num df	den df	missing info	riv
log10.body.mass	1419	1	6153	0.1201	0.1365
habitat	1.953	1	2290	0.1972	0.2457
log10.body.mass:habitat	0.3762	1	9181	0.09824	0.1089

	Pr(>F)
log10.body.mass	1.219e-279
habitat	0.1624
log10.body.mass:habitat	0.5397

Alternative approach: using MuMIn to do model averaging. Was it right to weight all of the models/trees equally?

pgls_avg <- model.avg(pgls_models, 
                      rank = function(x) 1)

This gives a model with the same coefficients (same model) that we can better make predict()ions from.

For the PGLS model, we also want to extract the estimate of \(\Lambda\), which tells us about how the phylogeny is affecting the correlation structure.

Simple approach: take the mean of the estimates of \(\Lambda\) from all the individual fitted models.

lambda <- mean(unlist(purrr::map(pgls_models, function(x) x$modelStruct$corStruct)))
lambda

## [1] -0.110112

Model Assessment

It’s not really clear how to even approach this, since we don’t really any longer expect the residuals to be normal or independent. And based on the data we know there’s not a huge issue with linearity. So…ok?

Mammal Stroke Volume

Fahlman & DeRuiter Labs

2021-07-27

Data

Read in data

Notes

Cleaning

Viz

GLS

Model Assessment

Model Predictions

Mixed-effects model

Model Assessment

Predictions from Model

PGLS

Model Assessment